1. Lesson 7.7 Adding and Subtracting Polynomials

2. California
Standards
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Student solve multistep problems, including word problems, by using these techniques.

3. Like terms are constants or terms with the same variable(s) raised to the same power(s).
Remember!

4. Adding Polynomials
Horizontal Method
Vertical Method

5. Add the polynomials.

6. When you use the Associative and Commutative Properties to rearrange the terms, the sign in front of each term must stay with that term.
Remember!

7. Opposite of a Polynomial
Simplify.

8. NOW YOU TRY…

9. Simplify.

10. Simplify.

11. Application
A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x2 + 7x – 5, and the area of plot B can be represented by 5x2 – 4x Write a polynomial that represents the total area of both plots of land.
(3x2 + 7x – 5)
Plot A. +
(5x2 – 4x + 11)
Plot B.
8x2 + 3x + 6
Combine like terms.

12. Write an expression that represents the area of
the shaded region in terms of x. 1)
x + 2 2) 3 5
x + 2 9 5 6
x + 2
3x + 7
2x + 5

13. Write an expression that represents the area of
the shaded region in terms of x. 1) 2) 5 8 3 7 3

14. Lesson Quiz: Part I Add or subtract. 1. 7m2 + 3m + 4m2
2. (r2 + s2) – (5r2 + 4s2)
3. (10pq + 3p) + (2pq – 5p + 6pq)
4. (14d2 – 8) + (6d2 – 2d + 1)
11m2 + 3m
–4r2 – 3s2
18pq – 2p
20d2 – 2d – 7
5. (2.5ab + 14b) – (–1.5ab + 4b)
4ab + 10b

15. Lesson Quiz: Part II
6. A painter must add the areas of two walls to determine the amount of paint needed. The area of the first wall is modeled by 4x2 + 12x + 9, and the area of the second wall is modeled by
36x2 – 12x + 1. Write a polynomial that represents the total area of the two walls.
40x2 + 10